OCHEM - Linear Combination of Atomic Orbitals

[persephone]

Homework Statement

Draw an LCAO representation of all of the bonding orbitals for C2H2O. Be sure to clearly state the hybridization of the two carbons and the oxygen in addition to drawing the orbital representation. Also show clearly what orbital any unshared pairs occupy.

Homework Equations

N/A

The Attempt at a Solution

I started out by drawing the molecular structure and came up with CH2=C=O where the 1st carbon has an sp2 hybridization, the 2nd carbon has an sp hybridization, and the oxygen has an sp2 hybridization.

I don't know where to go from here. I have seen LCAO representations but they have only been single bonds between two hydrogen atoms like the one on this site http://www.science.uwaterloo.ca/~cchieh/cact/fig/sigmah2.gif

How would I go about forming a Linear Combination of Atomic Orbitals with double bonds between the carbon-carbon and carbon-oxygen bonds, as well as the lone pairs?

Thank you!

 

[naele]

The first thing to do is recognize which is higher in energy, sigma or pi orbitals? Remember than sigma occurs with head on overlap while pi occurs with parallel overlap. Next is recognizing which is higher in energy, C=O or C=C. Also remember than for every atomic orbital you use, you get one molecular orbital, bonding and anti-bonding. Which is higher in energy, bonding or anti-bonding orbitals?

 

[Blueshift5]

To draw the LCAO representation for C2H2O, we first need to determine the valence electrons for each atom. Carbon has 4 valence electrons, while oxygen has 6. We also need to take into account the hybridization of each atom, as you have correctly stated.

For the first carbon, we have an sp2 hybridization which means that there are 3 orbitals available for bonding. These 3 orbitals will be used to form 3 sigma bonds - 1 with the other carbon and 2 with the oxygen. The remaining 1 p orbital will be used for the pi bond with the other carbon.

For the second carbon, we have an sp hybridization which means that there are 2 orbitals available for bonding. These 2 orbitals will be used to form 2 sigma bonds - 1 with the first carbon and 1 with the oxygen. The remaining 2 p orbitals will be used for the pi bond with the first carbon and the oxygen.

For the oxygen, we have an sp2 hybridization which means that there are 3 orbitals available for bonding. These 3 orbitals will be used to form 2 sigma bonds - 1 with each of the carbons. The remaining 1 p orbital will be used for the pi bond with the first carbon.

To draw the LCAO representation, we can use a combination of the atomic orbitals for each atom. For example, for the first carbon, we can use the sp2 hybrid orbital and one of the p orbitals to form the sigma bond with the oxygen. The remaining p orbital can be used to form the pi bond with the second carbon.

Similarly, for the second carbon, we can use the sp hybrid orbital and one of the p orbitals to form the sigma bond with the oxygen. The remaining p orbital can be used to form the pi bond with the first carbon.

For the oxygen, we can use the sp2 hybrid orbitals to form the sigma bonds with the carbons. The remaining p orbital can be used to form the pi bond with the first carbon.

To show the unshared pairs, we can simply indicate the remaining hybrid orbital on the oxygen atom.

The resulting LCAO representation for C2H2O would look like this:

[Image of LCAO representation for C2H2O]

In summary, to draw the LCAO representation